1Melt the butter in a large skillet over medium heat until it starts to foam. Add the shallots and reduce the heat to low. Cook, stirring occasionally, until the shallots are dark amber but not burned, about 30 minutes. Season with salt and pepper. (You can make these up to 1 week ahead and store in the fridge. Bring the shallots to room temperature before serving.)
2Preheat a grill or grill pan until very hot. Coat the steaks with oil and season generously with salt and pepper. Sear, without moving, until a dark golden crust forms, about 4 to 5 minutes. Flip and cook to the desired temperature, about 4 to 5 minutes more for medium rare (120°F on an instant-read thermometer). Let the steaks stand for 5 minutes before serving. Top with the caramelized shallots.